One-way sensitivity analysis
Identify which individual model inputs most influence incremental net monetary benefit over a chosen range.
Concepts and reasoning
Ask which assumptions can change the decision
A model result is conditional on its inputs. One-way sensitivity analysis asks what happens when one input moves across a specified range while every other input stays at its base-case value. It is useful for exposing influential assumptions, checking whether conclusions depend on a narrow numerical choice, and locating thresholds at which the preferred strategy changes.
The range is part of the question. A cost varied from 100 to 10,000 will usually produce a larger output range than the same cost varied from 900 to 1100. Therefore, the ranking in a tornado diagram is a ranking of the selected parameter–range combinations. It is not a universal ranking of biological importance, nor a ranking of which parameter should receive the most research funding.
A controlled change is not a probability distribution
The values in a deterministic sensitivity analysis may be confidence limits, plausible extremes, or scenario choices. Sweeping a grid over them does not make the grid points equally likely descriptions of reality. The proportion of grid points favoring an intervention is consequently not its probability of being cost-effective.
One-way analysis also holds relationships fixed that may change together in reality. For example, longer survival can increase both health benefit and downstream cost. Varying survival while artificially leaving every associated consequence unchanged may not describe a coherent scenario. When inputs are linked, vary the underlying relationship or define an explicit multi-parameter scenario. Probabilistic sensitivity analysis addresses a different question by sampling a specified joint distribution.
Mathematical foundations
Express the decision on a stable scale
Let
A decision threshold
If incremental cost is linear in a drug price,
For nonlinear models, calculate a grid and inspect the curve before assuming a single threshold. A curve can cross zero more than once or contain a discontinuity. Interpolation between distant grid points can then be misleading. Deterministic and probabilistic uses of sensitivity analysis are distinguished in the health-economic tutorial.
Worked example
Find the price at which a decision changes
Suppose a hypothetical treatment adds 0.15 QALYs, requires one course, and avoids 1000 in other costs. Let
| Additional course price | Incremental cost | INMB at 50,000 per QALY |
|---|---|---|
| 4000 | 3000 | 4500 |
| 6000 | 5000 | 2500 |
| 8500 | 7500 | 0 |
| 10000 | 9000 | −1500 |
The break-even price is 8500. A price below that level favors treatment under these assumptions; a higher price favors the comparator. This is not a market price recommendation, because quantities, health effects, implementation costs, and the threshold were stipulated for teaching.
If the threshold falls to 30,000, the break-even price becomes
Now imagine that price has a wide plausible range but utilities have been varied only ±1%. A tornado plot could rank price far above utility even if the true utility uncertainty were much larger. Before explaining the ranking, explain where each range came from.
Interpreting the results
Read sensitivity as a conditional comparison
A one-way analysis changes one input while holding the remaining assumptions at their base values. The span in incremental net monetary benefit indicates how much that particular change affects the decision at the selected threshold. A large span identifies influence over the specified range, not a probability that the input is wrong.
A range that crosses zero net benefit indicates that the preferred strategy can change within that interval. If both endpoints favor the same strategy, the decision is stable to those endpoint scenarios; it does not establish stability to every combined change or to nonlinear behavior between endpoints.
Rankings depend on the chosen ranges and output measure. An input with a narrow evidence-based interval may rank below a less influential input given an arbitrary wide interval. Report the base case, low/high input values, and resulting outcome changes together rather than presenting a ranking without its scale.
Assumptions and limitations
Respect linked parameters and constraints
Holding everything else fixed is only meaningful when that isolated variation represents a plausible scenario. Transition probabilities must still sum to one. Increasing one outgoing probability requires reducing another probability or defining a joint adjustment rule, and different rules can produce different results.
Costs, hazards, and utilities often share common evidence or functional relationships. Independent changes can break those relationships. One-way sensitivity is therefore a local exploration of assumptions, not a replacement for joint probabilistic uncertainty or structural scenarios.
Relative variation also behaves differently for zero and nonzero inputs: multiplying zero by any factor leaves it zero. A symmetric percentage range is not necessarily a credible uncertainty interval, particularly near probability boundaries. Choose ranges for their scientific interpretation rather than their visual symmetry.
Diagnostics and sensitivity analysis
Investigate influential and infeasible ranges
For the most influential inputs, inspect additional interior values and identify where net benefit changes sign. Endpoint comparisons can miss curvature and interactions. Recheck whether large changes are driven by a genuine mechanism, an inconsistent unit, or a correction to another linked parameter.
When a transition bound is infeasible, examine which probability became negative or exceeded one. Do not interpret a missing endpoint as zero effect. Either choose a defensible feasible range or revise the transition parameterization.
Repeat the analysis at relevant willingness-to-pay thresholds, because an input's influence on costs may matter differently from its influence on health. Follow important uncertainties with joint or structural sensitivity analysis. Document which quantities were varied and which were held fixed, including the rule used to balance transition rows.
References and other material
Read the methodological references and supporting tutorials below. The examples in this lesson are original teaching calculations, not findings from these sources.
- Cost-effectiveness analysis and decision modelling: a tutorial for clinicians — An introduction to economic decisions, trees and uncertainty.